Given design problems today, many organizations now implement Design for Six Sigma (DFSS) initiatives. One DFSS tool is quality function deployment (QFD), which is a design approach that proactively translates custome...
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Given design problems today, many organizations now implement Design for Six Sigma (DFSS) initiatives. One DFSS tool is quality function deployment (QFD), which is a design approach that proactively translates customers' needs into technical design requirements. The QFD methodology has been well documented in the literature, yet few researchers have investigated how this process may be used to solve multiresponse optimization problems. Here, we demonstrate a new approach that combines aspects of QFD within the traditional robust design methodology to address this issue. The methodology is demonstrated through an illustrated example, which is compared to the traditional robust design approach.
Sparse sequential quadratic programming (SQP) has offered fast and robust convergence of trajectory optimization based on direct collocation. However, the conventional approach of calculating the Hessian of the Lagran...
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Sparse sequential quadratic programming (SQP) has offered fast and robust convergence of trajectory optimization based on direct collocation. However, the conventional approach of calculating the Hessian of the Lagrangian is sometimes inefficient in view of the computational time. Therefore, this paper proposes two novel Hessian calculation methods that exploit the doubly-bordered block diagonal structure of the Hessian. Through applications to the constrained brachistochrone problem and the space shuttle reentry problem, the proposed methods were demonstrated to show faster convergence speeds as compared with the conventional methods.
In this comments paper, we revisit the network model introduced in [1]. We discuss the inaccuracy of the model and, to correct the network model, we propose to apply directed capacity constraints for directed flows. B...
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In this comments paper, we revisit the network model introduced in [1]. We discuss the inaccuracy of the model and, to correct the network model, we propose to apply directed capacity constraints for directed flows. Based on a comparison of numerical results, we show that the corrected model leads to better accuracy than the original model.
The purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases a...
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The purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases are performed in each iteration - the feasibility and the optimality phases. The first one directs the iterative process into the feasible region, i.e. finds one point with less constraints violation. The optimality phase starts from this point and its goal is to optimize the objective function into the satisfied constraints space. To evaluate the solution approximations in each iteration a scheme based on the filter method is used in both phases of the algorithm. This method replaces the merit functions that are based on penalty schemes, avoiding the related difficulties such as the penalty parameter estimation and the non-differentiability of some of them. The filter method is implemented in the context of the line search globalization technique. A set of more than two hundred AMPL test problems is solved. The algorithm developed is compared with LOQO and NPSOL software packages.
In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) is examined. The MSG is proposed by Gasimov for solving dual problems constructed with respe...
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ISBN:
(纸本)9789955282839
In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0-1 quadratic knapsack problem (QKP) is examined. The MSG is proposed by Gasimov for solving dual problems constructed with respect to sharp Augmented Lagrangian function. The MSG has some important proven properties. For example, it is convergent, and it guarantees the zero duality gap for the problems such that its objective and constraint functions are all Lipschtz. Besides it doesn't need to be convexity or differentiability conditions on the primal problem. The MSG has successfully used for solving nonconvex continuous and some combinatorial problems with equality constraints since it was suggested. In this study, the MSG is used to solve the QKP which is one of the well known combinatorial optimization problems with inequality constraint. Firstly, zero-one nonlinear problem is converted into continuous nonlinear problem by adding only one constraint and not adding new variables, then to solve the continuous QKP, dual problem with "zero duality gap" is constructed by using the sharp Augmented Lagrangian function. Finally, to solve the dual problem, the MSG is used by considering the equality constraint in the computation of the norm. The proposed approach is applied for some test problems. The results are also presented and discussed.
In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized ...
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In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007;25-52, 3-24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush-Kuhn-Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright (c) 2007 John Wiley & Sons, Ltd.
Here we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the centrality and the optimality presented in the op...
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Here we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the centrality and the optimality presented in the optimality conditions, and considers relaxed acceptability criteria for the step size and includes a feasibility restoration phase. Evaluation of the method has, until now, been made on small problems and a comparison is provided with a merit function approach.
Four step (sequential) procedures are traditionally used in forecasting travel on an urban transportation network. A typical transportation network consists of different trip purposes, user classes, and transportation...
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ISBN:
(纸本)9789889884734
Four step (sequential) procedures are traditionally used in forecasting travel on an urban transportation network. A typical transportation network consists of different trip purposes, user classes, and transportation modes. Due to the inconsistency results from the four step procedures, some research works proposed to combine these four step procedures. The resulting transportation model becomes a quite general supply-demand equilibrium problem which is a class of variational inequalities with a small number of asymmetric functions (also called combined model). Hence, we propose that Dantzig-Wolfe decomposition method should be used to divide the model into a small-scale equilibrium problem (variational inequalities) with the asymmetric functions and a large-scale symmetric transportation model (a nonlinear programming) with all of the details of network structure and trip demand.
Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is pr...
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Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.
In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earth-like planets around nearby stars. Because of limitations inherent...
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In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earth-like planets around nearby stars. Because of limitations inherent in the wave nature of light, the design problem is one of diffraction control so as to provide the extremely high contrast needed to image a faint planet positioned very close to its much brighter star. I will describe the mathematics behind the diffraction control problem and explain how modern optimization tools were able to provide unexpected solutions that actually changed NASA's approach to this problem.
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